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arXiv · 2308.05923

Genus one singularities in mean curvature flow

Adrian Chun-Pong Chu·Ao Sun
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Abstract

We show that for certain one-parameter families of initial conditions in $\mathbb R^3$, when we run mean curvature flow, a genus one singularity must appear in one of the flows. Moreover, such a singularity is robust under perturbation of the family of initial conditions. This contrasts sharply with the case of just a single flow. As an application, we construct an embedded, genus one self-shrinker with entropy lower than a shrinking doughnut.

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Adrian Chun-Pong Chu, Ao Sun. 2023-08-11. Genus one singularities in mean curvature flow. https://doi.org/10.2140/gt.2025.29.4299

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